Circle Theorems Watch this video https www youtube

Circle Theorems Watch this video https: //www. youtube. com/watch? v=Fc. OU 6 DF 876 M Task 1 Name the parts of the circle o Task 2 Name the parts of the circle. o Student response

Research Watch this video and make notes opposite https: //www. youtube. com/watch? v=Auiz. Rpe. JMhw Student response

Research Evidence Move the X and mark the angles asked for X X

Research Load the following https: //www. geogebra. org/m/Cc. Gtz 6 Qu Student response

Research Load the following https: //www. geog ebra. org/m/Uh. ZFP BXc Student response

Research Load the following https: //www. geogebra. org/m/v 5 b. Yc. TAM Student response

Research Angles in the same segment Theorem Load the following https: //www. ge ogebra. org/m/y yngv 6 u. C Student response

Research Cyclic Quadrilateral Theorem Load the following https: //www. geogebr a. org/m/ZYHXYCs. Q Student response

Research Angle in a semi circle Theorem Load the following https: //www. ge ogebra. org/m/y s. AEu. Kf. T Student response 1. Move points B and C until BC makes a diameter. 2. Move Point A. What do you notice about the angle at the circumference? 3. What type of triangles are AOD and BOD? How do we know this? 4. How can we use this to work out the missing angles?

You may find it helpful to watch this video to help with your research https: //www. youtube. com/watch? v=BDq. ELk 2 x. CPU Research Evidence For each question say which theorem you need to use to find x and find x

Student response

Student response

Consolidate Find the missing angles in each of the following questions Student response X= Y= Student response Student response Hint: you may need to use some other angle rules that you know

Consolidate Find the missing angles in each of the following questions Student response X= Y= Student response Student response Hint: you may need to use some other angle rules that you know and think of isosceles triangles made with radii of the circle

Exam Practice Model answer 1 Notice first that there is an isosceles triangle AOB because OA and OB are radii. Label the angle you want to find on the diagram. I’ve used x. Add the angles you find on the way to diagram too ANSWER: 122 58 29 x 90 Angle OAD =90 degrees because a tangent and radius meet at right angles Angle AOB = 58 degrees because angles in a triangle add up to 180 Angle AOB = 120 degrees because angles along a straight line equal 180 Angle OAB = 29 degrees because triangle AOB is isosceles Therefore angle CAB = 61 degrees because angles along the tangent add to 180

Exam Practice Model answer 2 90 x 56 34 56 90 Mark angle you want to find with an x Angle ACO is also 34 degrees. Two tangents meeting at a point are equal in length and so create a symmetrical kite when the points on the circle are joined to the centre. Angles OAC and OBC are 90 because radius and tangent Angles AOC and BOC are 56 degrees because angles in triangle Therefore angle DOA is 68 degrees because angles along a straight line add up to 180

Exam Practice • Complete exam questions using the following link https: //www. mathsgenie. co. uk/r esources/90_circle-theorems. pdf If you are able to, then you can print out the sheets to help you but everyone please make sure you write your answers here. This will be reviewed in lessons in September Student response